Exotic parametrization problems

The effects of parametrization on inverse problems

We consider two example systems, a logistic-growth population model and a damped spring-mass model. These models are each parameterized in two different ways. In one case (the logistic) the parameters are independent in one formulation and dependent in the other. In the other example (the spring-mass), the parameterizations are each independent. We carry out a series of inverse problems for the...

Cloud parametrization - Progress, Problems and Prospects

Processes that occur in clouds cover a wide range of spatial scales, from micrometers in the condensation and evaporation of individual cloud droplets through a few hundred meters in the case of fair weather cumulus clouds up to several hundred kilometers for the cloud systems associated with extratropical baroclinic systems. In order to describe the main effects clouds have on the atmosphere a...

Exotic Quantifiers, Complexity Classes, and Complete Problems

We introduce some operators defining new complexity classes from existing ones in the Blum-Shub-Smale theory of computation over the reals. Each one of these operators is defined with the help of a quantifier differing from the usual ones, ∀ and ∃, and yet having a precise geometric meaning. Our agenda in doing so is twofold. On the one hand, we show that a number of problems whose precise comp...

numerical solution of nonlinear optimal control problems based on state parametrization

in this paper, solution of nonlinear optimal control problems and the controlled duffing oscillator, as a special class of optimal control problems, are considered and an efficient algorithm is proposed. this algorithm is based on state parametrization as a polynomial with unknown coefficients. by this method, the control and state variables can be approximated as a function of time. also, the ...

Exotic Atoms and Exotic Nuclei